I think you should repot it into a larger pot with drainage holes (1, at most 2 sizes up) removing the mossy stuff at the top as you do it by pulling it all off, including some of the soil attached to it, without damaging the roots of the Jade plant. Use fresh potting soil to pack round the rootball and keep the soil level the same as it is now up the stems. More soil round the root ball means it will hang on to water for a little longer because the soil is not solid with roots, and have room to put out new roots and hopefully more, healthier growth.
In terms of watering, that mossy stuff indicates the soil is compacted and is not draining very well, another reason to repot. The best way to water is water the plant in immediately after repotting, allowing excess water to drain away freely from the base prior to placing it back in an outer pot or saucer. Ongoing, water when the surface of the soil feels just about dry to the touch, water well, again allowing excess to drain away freely, and make sure you empty the outer pot or tray 30 minutes after watering so the plant is not left sitting in water.
I can't see a 'white spot' on the base of any stem - just a strip of somewhat paler bark which may have been caused by the moss/lichen growth keeping it damp at times, but is nothing to worry about.